The magnetic flux through a coil of resistance '$$R$$' changes by an amount '$$\Delta \phi$$' in time '$$\Delta \mathrm{t}$$'. The total quantity of induced electric charge '$$\mathrm{Q}$$' is

A body weighs $$500 \mathrm{~N}$$ on the surface of the earth. At what distance below the surface of the earth it weighs $$250 \mathrm{~N}$$ ? (Radius of earth, $$\mathrm{R}=6400 \mathrm{~km}$$ )

Three discs $$\mathrm{x}, \mathrm{y}$$ and $$\mathrm{z}$$ having radii $$2 \mathrm{~m}, 3 \mathrm{~m}$$ and $$6 \mathrm{~m}$$ respectively are coated on outer surfaces. The wavelength corresponding to maximum intensity are $$300 \mathrm{~nm}, 400 \mathrm{~nm}$$ and $$500 \mathrm{~nm}$$ respectively. If $$\mathrm{P}_{\mathrm{x}}, \mathrm{P}_{\mathrm{y}}$$ and $$\mathrm{P}_{\mathrm{z}}$$ are power radiated by them respectively then

A stationary wave is represented by $$\mathrm{y}=10 \sin \left(\frac{\pi \mathrm{x}}{4}\right) \cos (20 \pi \mathrm{t})$$ where $$\mathrm{x}$$ and $$\mathrm{y}$$ are in $$\mathrm{cm}$$ and $$\mathrm{t}$$ in second. The distance between two consecutive nodes is